Question

Function A is a linear function that can be modeled by the equation 4x - 3y = 12.
Function B is a linear function whose graph passes through the points (4, 1) and (8, 4).
Complete the paragraph.

The y-intercept of Function A is____• the y-intercept of Function B. The slope of function A is ______the slope of Function B.

____= Less than, greater than or equal to

Answer 1

To find the y-intercept of Function A, we rearrange the equation \(4x - 3y = 12\) to the slope-intercept form \(y = mx + b\):

\[
-3y = -4x + 12 \\
y = \frac{4}{3}x - 4
\]

The y-intercept of Function A is \(-4\).

Next, we can find the slope of Function A, which is \(\frac{4}{3}\).

Now, let's find the slope of Function B using the points (4, 1) and (8, 4). The slope \(m\) is calculated as follows:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{8 - 4} = \frac{3}{4}
\]

Now we have all the necessary information:

- The y-intercept of Function A is \(-4\).
- The slope of Function A is \(\frac{4}{3}\).
- The slope of Function B is \(\frac{3}{4}\).

Now we can complete the paragraph:

The y-intercept of Function A is **less than** the y-intercept of Function B. The slope of Function A is **greater than** the slope of Function B.

**Answer:**

The y-intercept of Function A is **less than** the y-intercept of Function B. The slope of Function A is **greater than** the slope of Function B.